As Romina mentioned, it is always good to check with the embassy.
That said, did you know that there is a British-Irish visa scheme, which allows Indian nationals to travel under the same visa?
This means you won't need to apply for another visa.
There is more information regarding this scheme here
Let me know if you need any further help. I am sure you will enjoy your time in Dublin
, there is so much to do and visits there!